Question

Find the volume of the solid obtained by rotating the region bounded by
y = 1/x^4, y = 0, x = 1, x = 5
about the y-axis

Answer 1

@zepdrix I learned the disks/washers but not shells

Answer 2

@zepdrix yes

Answer 3

@zepdrix a little bit confusing, but i am haning on

Answer 4

@zepdrix i got a huge decimal 4.8001006.......

Answer 5

@zepdrix this is online homework, so i have an unlimited number of attempts to try to get the right answer and then it will tell me when i get it right

Answer 6

FYI,
Cylindrical shells seems to be a nicer approach


integrate from x= 1 to 5
\[ 2 \pi \int_1^5 x^{-3} \ dx = 2 \pi \cdot - \frac{1}{2} x^{-2} = -\frac{\pi}{x^2} \bigg|_1^5= \\ - \frac{\pi}{25} + \pi = \frac{24}{25} \pi = 0.96 \pi\]

using discs, you should get the same answer, though it is a bit more complicated.